Went on horseback round hot southern island (6)
I believe the answer is:
rhodes
'island' is the definition.
(Greek island)
'went on horseback round hot southern' is the wordplay.
'went on horseback' becomes 'rode' (I've seen this before).
'round' means one lot of letters goes inside another.
'hot' becomes 'h'.
'southern' becomes 's' (abbreviation).
'rode' placed around 'h' is 'rhode'.
'rhode'+'s'='RHODES'
(Other definitions for rhodes that I've seen before include "Colonial businessman" , "Greek island, ten miles off the Turkish coast" , "See 21 Down" , "British imperialist; Greek island" , "Island, explorer" .)